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A338025
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a(n) = LCM(k*j_1!*...*j_k! : j_1,...,j_k>=1, j_1+...+j_k=n, k=1,...,n)/n!.
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2
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1, 1, 2, 1, 6, 2, 6, 3, 10, 2, 6, 2, 210, 30, 12, 3, 30, 10, 210, 42, 330, 30, 60, 30, 546, 42, 28, 2, 60, 4, 924, 231, 3570, 210, 6, 2, 51870, 2730, 420, 42, 2310, 330, 4620, 210, 9660, 420, 420, 210, 6630, 1326, 1716, 66, 660, 220, 1596, 114, 1740, 60, 60, 12, 1861860, 60060
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OFFSET
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1,3
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COMMENTS
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For each prime p >= 2, the exponent of p in a(n) is the largest integer t such that p^t is less than or equal to the sum of digits of n in base p.
n!*a(n) is the smallest common denominator of the n-th degree coefficients of the Baker-Campbell-Hausdorff series.
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LINKS
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FORMULA
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MAPLE
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A338025 := n->mul(map(p->p^(ilog[p](add(i, i=convert(n, base, p)))), select(isprime, [seq(p, p=2..n)]))):
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PROG
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(Julia)
using Primes
prod([p^(floor(Int, log(p, sum(digits(n, base=p)))))
for p in 2:n if isprime(p)])
(PARI) a(n) = {my(v = matrix(primepi(n), 2, i, j, my(p=prime(i)); if (j==1, p, logint(sumdigits(n, p), p)))); factorback(v); } \\ Michel Marcus, Oct 08 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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